Timber is the word we use in Australia, Britain, and lumber is what Americans call the material. Trees are made from wood, and when the wood is processed it is called timber/lumber. The word "timber" is allied to 'zimmer' a room, 'dom/ дом" a house, and the "domestic" words that come from it. It infers a building material, not raw wood/logs.
You can buy lumber in a lumberyard, but we call it here timber in a timber yard, but it's the same thing. Wood is a general word for the untreated, unprocessed raw material.